Derivation of the Christoffel symbol

[Whitehole]

I'm reading Zee's Gravity book, can anyone help me understand the explanation on this part,

I understand everything except the last part, he said to use (I.4.14) so that I could solve for the quantity shown in the image, what does he mean by that and how?

 

[jedishrfu]

I don't know the answer to your question, I remember seeing this video on YouTube that "derived" Einstein Field equations and did some technique to extract the Christoffel symbols out. It may help you understand what Zee has done as well: